The present invention relates generally to a method of deriving compositional information. More specifically, the present invention relates a method of deriving accurate compositional information from a multi-layer composition.
Beta gauges are nuclear measuring devices which emit beta rays, and which have been used to measure characteristics of single-layer compositions, such as single-layer plastic films. For example, beta gauges have been used to measure the mass and/or thickness of these single-layer compositions.
Typically, a single-layer composition, such as a single-layer plastic film, has a known beta ray absorption coefficient (represented as a nominal composite KCM) and a known density. Using a beta gauge, the mass per unit area (usually represented as grams per square meter, or gsm) of the single-layer plastic film can be determined. That is, by multiplying the relatively accurate, raw output of the beta gauge by the known absorption coefficient of the single-layer plastic film, the mass per unit area can be calculated for each point on the film to be measured. Similarly, the thickness of the single-layer plastic film may be measured at each such point. The thickness of a point on the film corresponds to the mass per unit area of that point, as previously determined, divided by the known density of the plastic used to form the film.
Because the absorption coefficient and density for a given plastic are known with a relatively high accuracy, the beta gauge is relatively accurate in determining such characteristics as mass and thickness for a single-layer plastic film. For single-layer or single-component samples, the intrinsic accuracy of the beta gauge is approximately a quarter of a percent. That is, the output of the beta gauge can be used to calculate both the mass and the thickness of a single-layer plastic film to within a quarter of a percent.
However, the accuracy of the beta gauge deteriorates when a composition formed of multiple layers of different plastics is measured. For different plastics, the absorption coefficient for the beta rays varies. Similarly, the densities of different plastics are not the same. For example, the absorption of beta rays by different plastics can vary by as much as 4 to 5 percent. The densities of various plastics can vary by as much as 30 percent.
Thus, if a composition is formed from a plurality of layers of different materials, then the composite absorption coefficient for the entire multi-layer composition is unknown. If a composite absorption coefficient for the multi-layer material is merely estimated based on the range of potential values as mentioned above, then the total mass measurement of the multi-layer composition using a beta gauge could be off by as much as 4 to 5 percent. That is, because the mass of a composition is measured by multiplying the output of the beta gauge by the absorption coefficient and because the range of absorption coefficients for different plastics can vary as much as 4 to 5 percent, the accuracy of the beta gauge is limited to 4 to 5 percent in determining the mass of a multi-layer plastic. Typically, however, the beta gauge deteriorates from its quarter of a percent accuracy to approximately a 2 percent range of accuracy, since the particular plastics used to form a given multi-layer composition may have absorption coefficients which only vary in range by 2 percent.
Similarly, the accuracy of the beta gauge deteriorates when the gauge is used to measure the thickness of a multi-layer composition such as a multi-layer plastic film. As described above, the thickness of such a film can be determined by dividing the mass per unit area at a point on the film (as determined with the beta gauge and the absorption coefficient of the film) by the density of the plastic used to form the film. However, the accuracy of the beta gauge's mass determination for multi-layer compositions is relatively inaccurate, as was mentioned above. Furthermore, as with the absorption coefficient, the density of a multi-layer composition is not known with great accuracy.
That is, although the densities for the individual layers of a multi-layer plastic are known, the overall density for a given combination of plastic layers is not known. Rather, only the range of the densities for the various layers is known. As was mentioned above, the densities of the various layers in a multi-layer composition can vary by as much as 30 percent or more for different combinations of plastics.
Because the use of a beta gauge results in a mass per unit area measurement which is only known with approximately a 4 to 5 percent accuracy, and because the density of a multi-layer composition is only known with approximately a 30 percent accuracy, the compositional information such as the thickness of a multi-layer plastic which is derived from a beta gauge output is extremely limited in accuracy. Although the thickness derived from a beta gauge could be off by as much as 30 percent, a 5 to 10 percent error is typical. The accuracy of the information derived from a beta gauge deteriorates to a greater extent as the number of layers of different materials used to form the multi-layer composition is increased.
Such inaccuracies in the information derived from a beta gauge for a particular multi-layer composition are extremely serious. That is, a range of errors from 5 to 30 percent for multi-layer compositions is significantly greater than the subpercent accuracy which is typically associated with the use of a beta gauge for single-layer plastics.
The beta gauge's characteristics thus result in significantly less accurate readings when measuring compositions such as multi-layer plastic film constructions. This is especially true when mass and thickness measurements are required. The inaccuracy results from the fact that the relative composition of a multi-layer film varies. Therefore, the use of a single standard sample obtained from a multi-layer plastic sheet or film to derive mass and thickness measurements would not represent the composition of many or most of a sheet or film being produced. That is, the values for the beta gauge's primary calibration coefficients, (i.e., the absorption coefficient (KCM) and the density), would be accurate for the single standard sample but would not be accurate for most of the sheet or film which has been produced. The absorption coefficient and the composite density vary between such common low-density resins as polypropylene (PP) or polyethylene (PE), and such high-density, heteroatom-containing resins as nylon or polymethyl methacrylate (PMMA). Thus, relevant values for a composite absorption coefficient and a composite density of a multi-layer film can only be calculated if the composition of the film is known at each point on the film.
One area where improved accuracy in such compositional information as mass and thickness would be desirable is in the production of a multi-layer film or sheet as referred to above. Here, it is often desirable to maintain a tight tolerance on total film thickness both across the film as well as along the film. However, a thickness profile calculated from a beta gauge alone is extremely inaccurate for a multi-layer film. Attempts to modify the ratio of one layer to the next during the production of such a multi-layer film using, for example, the single standard sample referred to previously, merely result in false, or improper, thickness adjustments.
Accordingly, there is a need for a method of obtaining compositional information for multi-layer compositions, such as multi-layer plastics, which approaches the accuracy of the measurements derived for single-layer compositions.